6S Linear Programming McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All Learning Objectives  Describe the type of problem tha would lend itself to solution using linear programming  Formulate a linear programming model from a description of a problem  Solve linear programming problems using the graphical method  Interpret computer solutions of linear programming problems  Do sensitivity analysis on the solution of a linear progrmming problem 6S-2 Linear Programming  Used to obtain optimal solutions to problems that involve restrictions or limitations, such as:  Materials  Budgets  Labor  Machine time 6S-3 Linear Programming  Linear programming (LP) techniques consist of a sequence of steps that will lead to an optimal solution to problems, in cases where an optimum exists 6S-4 Linear Programming Model  Objective Function: mathematical statement of profit or cost for a given solution  Decision variables: amounts of either inputs or outputs  Feasible solution space: the set of all feasible combinations of decision variables as defined by the constraints  Constraints: limitations that restrict the available alternatives  Parameters: numerical values 6S-5 Linear Programming Assumptions  Linearity: the impact of decision variables is linear in constraints and objective function  Divisibility: noninteger values of decision variables are acceptable  Certainty: values of parameters are known and constant  Nonnegativity: negative values of decision variables are unacceptable 6S-6 Graphical Linear Programming Graphical method for finding optimal solutions to two-variable problems Set up objective function and constraints in mathematical format Plot the constraints Identify the feasible solution space Plot the objective function Determine the optimum solution 6S-7 Linear Programming Example  Objective - profit Maximize Z=60X1 + 50X2  Subject to Assembly 4X1 + 10X2